Centerfire ammunition cartridges generally include a case, a bullet seated in a mouth of the case, a propellant inside the case, and a primer seated in the primer pocket of the case for igniting the propellant. In some cartridges, the primer pocket is crimped to secure the primer in the primer pocket. The crimp is usually made by deforming a side wall of the primer pocket inward to protrude against the primer. After such a cartridge is fired, if it is desired to reload the case, the primer pocket usually needs to be swaged to prepare the primer pocket for receipt of a new primer. Sometimes uncrimped cases are swaged to properly size the primer pockets. Various devices are known for swaging primer pockets. In general, a swaging pin is pushed into the primer pocket. A head of the swaging pin is sized to expand the crimped portion of the primer pocket to provide the primer pocket with a relatively smooth side wall. Insertion of the new primer is then much easier and reloading results are improved.